A331037 Numbers k such that the sum of the divisors of k (except for 1 and k) plus the sum of the digits of k is equal to k.

1, 2, 3, 5, 7, 14, 52, 76, 2528, 9536, 9664, 35456, 138496, 8456192, 33665024, 33673216, 537444352, 2148958208, 137454419968

Offset

1,2

Comments

Additional terms include 537444352, 2148958208, 137454419968, 35184644718592, 9007202811510784. Are there any terms > 1 not of the form 2^k*p where p is prime and k>0? - David A. Corneth, Jan 08 2020

Terms not of the form 2^k*p do exist, for example 2^15*65713*24194197 and 2^19*1739719*2639431. - Giovanni Resta, Jan 08 2020

a(20) > 10^13. - Giovanni Resta, Jan 14 2020

Links

Table of n, a(n) for n=1..19.

Example

The first term that is not 1 or a single-digit prime is obtained by adding the proper divisors of 14 other than 1 (2,7) to its digits (1,4): (2+7) + (1+4) = 14.
The second such term is 52: the proper divisors of 52 other than 1 (2,4,13,26) and its digits (5,2) sum to (2+4+13+26) + (5+2) = 52.

Mathematica

Select[Range[10^7], DivisorSigma[1, #] - # - If[# == 1, 0, 1] + Plus @@ IntegerDigits[#] == # &] (* Amiram Eldar, Jan 12 2020 *)

Prog

(PARI) is(n) = n == sigma(n)-1-if(n>1, n, 0)+sumdigits(n) \\ Rémy Sigrist, Jan 08 2020

Crossrefs

Cf. A000203, A007953, A048050.

Cf. A331093 (sum of divisors - digit sum = the number).

Sequence in context: A324840 A316475 A303875 * A228652 A157833 A175758

Adjacent sequences: A331034 A331035 A331036 * A331038 A331039 A331040

Keyword

nonn,base,more,less

Author

Joseph E. Marrow, Jan 08 2020

Extensions

a(14)-a(16) from Rémy Sigrist, Jan 08 2020

a(17)-a(19) from Giovanni Resta, Jan 14 2020

Status

approved